エルミート行列の同時対角化のある一般化とその量子推定理論との関係について
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概要
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We study the problem of minimizing a quadratic quantity defined for given two Hermitian matrices X, Y and a positive-definite Hermitian matrix. This problem is reduced to the simultaneous diagonalization X, Y when XY=YX. We derive a lower bound for the quantity, and in some special cases solve the problem by showing that the lower bound is achievable. This problem is closely related to a simultaneous measurement of quantum mechanical observables which are not commuting and has an application in the theory of quantum state estimation.
- 一般社団法人日本応用数理学会の論文
- 1991-12-15